A Generalized Gaussian Process Model for Computer Experiments With Binary Time Series

Abstract

Non-Gaussian observations such as binary responses are common in some computer experiments. Motivated by the analysis of a class of cell adhesion experiments, we introduce a generalized Gaussian process model for binary responses, which shares some common features with standard GP models. In addition, the proposed model incorporates a flexible mean function that can capture different types of time series structures. Asymptotic properties of the estimators are derived, and an optimal predictor as well as its predictive distribution are constructed. Their performance is examined via two simulation studies. The methodology is applied to study computer simulations for cell adhesion experiments. The fitted model reveals important biological information in repeated cell bindings, which is not directly observable in lab experiments. Supplementary materials for this article are available online.

Keywords:

• Computer experiment
• Gaussian process model
• Single molecule experiment
• Uncertainty quantification

Supplementary Materials

The assumptions for Theorems 3.1 and 3.3, the proofs of Theorems 3.1, 3.3, 4.1, 4.3, and the algorithms for estimation and emulation are given in an online supplement.

Acknowledgments

The authors gratefully acknowledge helpful advice from the associate editor and two referees.

Additional information

Funding

This work was supported by NSF DMS 1660504 and 1660477.